A013618 Triangle of coefficients in expansion of (1+11x)^n.

1, 1, 11, 1, 22, 121, 1, 33, 363, 1331, 1, 44, 726, 5324, 14641, 1, 55, 1210, 13310, 73205, 161051, 1, 66, 1815, 26620, 219615, 966306, 1771561, 1, 77, 2541, 46585, 512435, 3382071, 12400927, 19487171, 1, 88, 3388, 74536, 1024870, 9018856, 49603708, 155897368, 214358881

Offset: 0

Author

N. J. A. Sloane

Keywords

• tabl
• nonn
• easy

Comments

T(n,k) equals the number of n-length words on {0,1,...,11} having n-k zeros. - Milan Janjic, Jul 24 2015

Links

• Seiichi Manyama, Rows n = 0..139, flattened

Crossrefs

Cf. A001020 (right edge).

Programs

Maple

T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+11*x)^n):
seq(T(n), n=0..10);  # Alois P. Heinz, Jul 24 2015

Formula

G.f.: 1 / (1 - x(1+11y)).

T(n,k) = 11^k*C(n,k) = Sum_{i=n-k..n} C(i,n-k)*C(n,i)*10^(n-i). Row sums are 12^n = A001021. - Mircea Merca, Apr 28 2012